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Find the distance from the Earth's surface at which the acceleration due to gravity has the same value whether you go that distance above the surface or below it. (R is the Earth's radius.)

1. x = R(sqrt(5) - 1)/2
2. x = R/2
3. x = R(sqrt(5) + 1)/2
4. x = R/3

Correct answer: x = R(sqrt(5) - 1)/2

Solution

Equate the gravity value at height x above the surface to the value at depth x below, then solve the resulting algebraic equation.

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